Question

2. ONLY ANSWER QUESTION 3 According to the empirical rule, approximately what percentage of normally distributed data lies within one standard deviation of the mean?

3. An auto manufacturer claims that its new 4-cylinder Hybrid auto with manual shift averages 50 mpg under city driving conditions. A Federal Agency believes this claim is too high and decides to randomly test 25 of the manufacturer's 4-cylinder Hybrid autos with manual shift. The Agency determines the mean average mpg for the sample to be 48 with a sample standard deviation of 4 mpg under city driving conditions. The p-value for this hypothesis test is:

Answer 1

Hypothesized mean, $\mu$ = 50 mpg

Sample mean, = 48 mpg

T

Sample standard deviation, s = 4 mpg

Standard error of mean, SE = s /
n
= 4 / $\sqrt{25}$ = 0.8 mpg

Test statistic, t = (
T
- $\mu$ ) / SE = (48 - 50) / 0.8 = -2.5

Degree of freedom = n-1 = 25-1 = 24

P-value = P(t < -2.5, df = 24) = 0.0098